Suarez appeared to handle the ball before netting to put Liverpool 2-0 up and Radford said that the decision to allow the goal has "stolen" their chance of a replay.
"I have enjoyed the day but it feels like it was stolen from us, whether it was deliberate or not," Radford told ESPN. "I feel it should be sorted out, we put up a sterling effort and we are proud of ourselves.
"It was not in our favour and we should have had at least a replay. Handballs are obviously de rigueur in this game we play."
Liverpool will now face a trip to Oldham Athletic in the fourth round.